Optical coherence tomography (OCT) is an optical imaging technology for performing in situ real-time cross-sectional imaging of tissue structures at a resolution of less than 10 microns. OCT measures the scattering profile of a sample along the OCT beam. Each scattering profile is called an axial scan, or A-scan. Cross-sectional images, called B-scans, and by extension 3D volumes, are built up from many A-scans, with the OCT beam moved to a set of transverse locations on the sample.
In recent years, it has been demonstrated that Fourier domain OCT (FD-OCT) has advantages over the original time-domain OCT (TD-OCT) (R. A. Leitgeb et al. (2003). “Performance of fourier domain vs. time domain optical coherence tomography.” Optics Express 11(8): 889-94; J. F. de Boer et al. (2003). “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography.” Optics Letters 28(21): 2067-2069; M. A. Choma et al. (2003). “Sensitivity advantage of swept source and Fourier domain optical coherence tomography.” Optics Express 11(18): 2183-89). In TD-OCT, the optical path length between the sample and reference arms needs to be mechanically scanned. In FD-OCT, on the other hand, the optical path length difference between the sample and reference arm is not mechanically scanned. Instead, a full A-scan is obtained in parallel for all points along the sample axial line within a short time, determined by the wavelength sweep rate of a swept source in swept-source OCT (SS-OCT) or the line scan rate of the line scan camera in spectral-domain OCT (SD-OCT). As a result, the speed for each axial scan can be substantially increased as compared to the mechanical scanning speed of TD-OCT.
Even with the increased speed of FD-OCT, however, the accuracy of OCT for a number of ophthalmic applications can be limited by the effect of motion during data acquisition. These applications include pachymetry, keratometry, and corneal power calculations.
Pachymetry
Pachymetry is the measurement of corneal thickness. Corneal thickness can be important in assessing corneal diseases, intraocular pressure, ocular hypertension, and a patient's eligibility for refractive surgical procedures (Y. Li et al. (2010). “Pachymetric mapping with Fourier-domain optical coherence tomography.” J. Cataract Refract. Surg. 36(5): 826-31, hereby incorporated by reference). The use of optical coherence tomography (OCT) to generate pachymetry maps has been well demonstrated using both time-domain and Fourier-domain OCT systems (see for example Y. Li et al. (2010)). Pachymetry maps are generated by calculating the corneal thickness along each of these scans. It is desirable to obtain high density pachymetry maps by either acquiring more meridional scans, or by sampling the cornea more densely, as it minimizes the probability of missing smaller regions of pathology. However, denser sampling would require a longer scan time, and would, in turn, make the data more susceptible to eye motion. A method for generating a denser pachymetry map without motion-related error would therefore be desirable.
Keratometry
Keratometry is the measurement of the curvature of the anterior surface of the cornea. A number of different instrument types can be used to determine the curvature. Often, measurements are taken not by true keratometers but by corneal topographers, which provide simulated keratometry (Sim-K) readings. These do not directly measure the x, y, and z coordinates of the points on the corneal surface, but instead generally use the reflection of incident light by the cornea to measure its shape. The most popular type of modern corneal topographer is the Placido system, which projects multiple light concentric rings on the cornea. The reflection is captured, and then the height of each point of the cornea is extrapolated from the reflection. Computer software and algorithms can analyze the data and display the results in various maps; typically they measure the deviation of reflected rings and calculate the curvature of the corneal surface points in the axial direction, which can then be used to compute Sim-K.
Sim-K measurements characterize curvatures in the central 3 mm area of the cornea. The measurements are essentially what a manual keratometer would estimate the corneal curvature to be at approximately the 3 mm zone. The measurements generated by simulated keratometry include the curvature and axes of the steepest and flattest meridians of the cornea. The steep Sim-K is the steepest meridian of the cornea, based on samples along the central pupil area with 3-mm diameter. The flat Sim-K is the flattest meridian of the cornea and is by definition 90° apart from the steepest meridian. These readings provide the central corneal curvature that is visually most significant. Sim-K is valuable for detection of postoperative astigmatism, planning of removal of sutures, and postoperative fitting of contact lenses.
Corneal topography, however, has certain limitations. For example, it requires an intact epithelial surface and tear film to neutralize corneal irregularities. Also, error can arise from problems caused by misalignment and fixation error that amplify measurements of astigmatism, which decreases the accuracy of the corneal measurements. It can also be difficult to calculate the position of the center from the small central rings, and there can be increased inaccuracy toward the periphery because the accuracy of each point depends on the accuracy of all preceding points.
Under optimal conditions, the error of corneal topography is around ±0.25 D. However, the errors can be significantly higher in abnormal corneas—often ±0.50-1.00 D (see for example A. K. Gupta (2012). Clinical Ophthalmology: Contemporary Perspectives). Thus, there is a need for a method of measuring the curvature of the cornea with greater accuracy, especially in abnormal corneas. Although OCT is currently being used to calculate net central corneal power (see D. Huang (2012). “Corneal power and IOL power calculation with OCT,” presentation to Taiwan Academy of Ophthalmology, available at http://www.coollab.net/fileadmin/coollab_upload/coollab/docs/1Huang-OCT-based_IOL_formula-taiwan.pdf), the methods described here would allow additional metrics to be determined as well, which may be useful for refractive surgery planning. This method may also allow existing formulas for intraocular lens (IOL) power calculation (see for example K. J. Hoffer (1993). The Hoffer Q formula: a comparison of theoretic and regression formulas. J. Cataract Refract. Surg. 19(6): 700-12) to be used, since the corneal power is calculated by similar models as those in existing devices such as IOL Master (Carl Zeiss Meditec, Inc. Dublin, Calif.).
Corneal Power
Accurate measurement of corneal power is essential for various diagnostic and therapeutic applications in ophthalmology. Standard keratometers determine posterior corneal power by extrapolating based on the assumption of a fixed keratometric index, which is in turn based on the assumption of a fixed ratio between anterior and posterior curvature. This assumption of a fixed ratio leads often to incorrect results when changes in surface curvature occur mostly at the anterior corneal surface—for instance, due to pathology or refractive surgery. This assumption can thus lead to incorrect corneal power determinations (M. Tang et al. (2010). “Corneal power measurement with Fourier-domain optical coherence tomography.” J. Cataract Refract. Surg. 36(12): 2115-22).
Instead of manual or simulated keratometry, OCT data can be used to determine corneal power. Using two-dimensional OCT cross-sectional scans to determine corneal power by measuring the radius of curvature of anterior and posterior corneal surfaces has been suggested and demonstrated (see, for example, M. Tang et al. (2010); U.S. Pat. No. 7,878,651 to O'Hara et al.). Existing methods calculate corneal power by using least squares to determine a parabolic fit to each meridional scan over the central 3 mm diameter area. The powers of each meridian are then averaged to obtain the anterior, posterior, and net corneal powers.
One of the biggest challenges, however, in using OCT B-scans for calculating the corneal power is the error in curvature measurements caused by motion of the cornea in the z and transverse directions. Small movements can cause significant errors in power calculations. For example, a z displacement of 1.3 μm while the scan beam moves 1 mm from the vertex will result in error of approximately 1 diopter in corneal power. O'Hara et al. suggest techniques for z-motion correction by using Doppler signal and by measuring displacement of a single point during repeated scans. However, any translational movement of the pupil may reduce the effectiveness of the z-correction. It is true that the effect of translational motion perpendicular to the B-scan direction would cause errors of relatively lower magnitude. Nonetheless, the effect for lateral motion cannot be neglected for high accuracy measurements of corneal curvature. Even at the vertex, where the lens sag due to transverse motion is at a minimum, a displacement of 200 μm could cause an error of approximately 1.84 diopters in measurements. This error will only increase with greater distance from the vertex of the cornea.
The power computation may also be inaccurate in corneas with pathology or after refractive surgery. In these cases, the corneal surface in the 3 mm diameter region may not be modeled accurately using a parabolic model fit. Therefore, a robust and accurate fitting method is essential for accurate corneal power computation. Thus, although OCT is capable of directly measuring both corneal surfaces, a method of using OCT for corneal power measurements that has acceptable accuracy and repeatability is desirable.
Tracking and Registration
Active and accurate corneal surface tracking and registration are important for the applications described here. Accurate change analysis of measurements from multiple visits (e.g. before and after corneal surgery) is essential for comparing the difference in pachymetry or epithelial maps. Thus, accurate corneal surface registration becomes an inevitable preprocessing step in the change analysis. Also, axial curvature maps (from multiple visits) that determine the radius of curvature of the cornea at each measured point, and resulting Sim-k values, as well as corneal power calculations, will not be repeatable and comparable between different visits without proper registration. Tracking and registration can also be incorporated into an efficient alignment of OCT-based acquisition systems, improve the repeatability of anterior segment measurement, and enhance laser eye surgery systems and techniques by aiming to reduce the effect of patient eye movement.
Existing tracking methods for OCT systems generally involve locating an iris, pupil center, a corneal vertex, and/or at least one reflection on the image. A computer processor having a program computes the position of the iris or pupil center on an image of the eye, or the position of a corneal vertex from a series of OCT B-scans. Like existing tracking methods, existing registration methods involve using the pupil or corneal vertex as the centration landmark. These methods are problematic because the corneal vertex depends on the eye's fixation to a specific target. Orientation of the corneal surface also depends on the eye's fixation to a specific target, but these techniques neglect the eye's rotation around three axes. Thus, there is a need for tracking and registration methods that take the corneal surface rotation about three axes into consideration and that rely on a fixed position on the corneal surface. One such fixed position whose use as a reference point would improve tracking and registration is the corneal apex.